Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2142 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #71565 | C2 | semidirect |
| 11. C22×C3×C4⋊C4 | C4 | semidirect |
| 58. C22×C4⋊C4 | Dic3 | semidirect |
| 89. C22×C3×C4 | C4⋊C4 | semidirect |
| 199. C22×C4 | C4⋊Dic3 | semidirect |
| 304. C3 | #14339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4⋊C4 | 2 |
| C2×#5211 | 2 |
| C2×#5212 | 2 |
| #72127 | 2 |
| #71565 | 2 |
| #14339 | 3 |